What is the solution for y^'=((x^2y+y^3))/(x^3) ?

The solution for y^'=((x^2y+y^3))/(x^3) is y= x/(sqrt(-2ln(x)+c_{1))},y=-x/(sqrt(-2ln(x)+c_{1))}

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y^'=((x^2y+y^3))/(x^3)

y^{^{'}} = \frac{( x ^{2} y + y ^{3} )}{x ^{3}}

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

Solution steps

y^{'} (x) = \frac{( x ^{2} y + y ^{3} )}{x ^{3}}

Solve Bernoulli ODE:

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

y = \frac{x}{- 2 ln ( x ) + c _{1}}, y = - \frac{x}{- 2 ln ( x ) + c _{1}}

\int_{1}^{5} \frac{ln ( x )}{x ^{3}} d x

\int x + 0.5 d x

\frac{1}{1 - x}, - 1

\int 3 9 x d x

\frac{d}{d x} (\frac{( 1 + x )}{1 - x})

What is the solution for y^'=((x^2y+y^3))/(x^3) ?
The solution for y^'=((x^2y+y^3))/(x^3) is y= x/(sqrt(-2ln(x)+c_{1))},y=-x/(sqrt(-2ln(x)+c_{1))}